Cornyn is the first of a handful of GOP stalwarts — including Senate Minority Leader Mitch McConnell of Kentucky and veteran appropriator Thad Cochran of Mississippi — trying to fend off an insurgent Republican with Tea Party support. The Texas primary is March 4 and kicks off the 2014 midterm election season. These generational and ideological battles are among the themes playing out this year as Republicans try to gain control of the Senate.

In the Lone Star state’s other marquee race this year, Attorney General Greg Abbott has an 11-point lead over state Sen. Wendy Davis for governor among Texas adults, the poll shows.

Abbott, a Republican, and Davis, the Democrat who shot to national fame with her filibuster of an abortion bill, are both leading their rivals for their respective party nominations — so the real battle for Texas governor will come during the general election in the fall. Abbott has had to answer questions about the support he’s received from controversial rocker Ted Nugent, while Davis has had to explain discrepancies in her biography.

The winner will succeed retiring Gov. Rick Perry, who is eyeing another presidential bid.